Quantum data loader

Abstract

This disclosure relates generally to the field of quantum algorithms and quantum data loading, and more particularly to constructing quantum circuits for loading classical data into quantum states which reduces the computational resources of the circuit, e.g., number of qubits, depth of quantum circuit, and type of gates in the circuit.

What is claimed is: 
     
       1. A quantum circuit for use in encoding a first n-dimensional vector representing classical data into a first quantum state, encoding a second n-dimensional vector representing classical data into a second quantum state, and determining a distance between the first n-dimensional vector and the second n-dimensional vector, the quantum circuit comprising:
 2n qubits; 
 a first layer comprising an X gate applied to one of the 2n qubits; 
 a first group of subsequent layers that applies BS gates to the 2n qubits according to a binary tree pattern, wherein each BS gate is a single parametrized 2-qubit gate; and 
 an additional layer after the first group of subsequent layers that applies BS gates in parallel to pairs of qubits of the 2n qubits, wherein a first qubit in a pair is associated with the first quantum state and a second qubit in the pair is associated with the second quantum state, 
 wherein a number of layers including the first layer, the first group of subsequent layers, and the additional layer is not more than ceiling(log 2  (n)+3). 
 
     
     
       2. The quantum circuit of  claim 1 , wherein n is a power of 2. 
     
     
       3. The quantum circuit of  claim 1 , wherein a root node of the binary tree pattern is the qubit that the X gate is applied to. 
     
     
       4. The quantum circuit of  claim 1 , wherein a total number of qubits in the quantum circuit is not greater than 2n. 
     
     
       5. The quantum circuit of  claim 1 , wherein a total number of BS gates in the quantum circuit is not greater than 3n−1. 
     
     
       6. The quantum circuit of  claim 1 , wherein a number of layers of the first group of subsequent layers is a logarithmic number of n. 
     
     
       7. The quantum circuit of  claim 1 , wherein each BS gate in the first group of subsequent layers has a form:
     BS (θ j )=[[1,0,0,0],[0,cos(θ j ),sin(θ j ),0],[0,−sin(θ j ),cos(θ j ),0],[0,0,0,1]],
 
 
       where θ j  is an angle and j is an integer indicating a location of the BS gate in the binary tree pattern of the first group of subsequent layers. 
     
     
       8. The quantum circuit of  claim 7 , wherein 
       
         
           
             
               θ 
               = 
               
                 arccos 
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                 ( 
                 
                   
                      
                     x 
                      
                   
                   
                     
                       
                         
                            
                           x 
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           y 
                            
                         
                         2 
                       
                     
                   
                 
                 ) 
               
             
           
         
       
       for a first BS gate of the binary tree, wherein the first n-dimensional vector is (x 1 , x 2 , . . . , x n ), where x i  is a real number, the second n-dimensional vector is (y 1 , y 2 , . . . , y n ), where y i  is a real number, and the Euclidean norms of the first and second vectors are respectively ∥x∥ 2 =Σ i=1   n |x i | 2  and ∥y∥ 2 =Σ i=1   n |y i | 2 . 
     
     
       9. The quantum circuit of  claim 7 , wherein θ=π/4 for BS gates in the additional layer. 
     
     
       10. The quantum circuit of  claim 1 , wherein a probability of observing all zeros in the first n qubits is equal to the distance between the first n-dimensional vector and the second n-dimensional vector divided by four. 
     
     
       11. A quantum circuit for use in encoding a first n-dimensional vector representing classical data into a first quantum state, encoding a second n-dimensional vector representing classical data into a second quantum state, and determining a distance between the first n-dimensional vector and the second n-dimensional vector, the quantum circuit comprising:
 n qubits; 
 a first layer comprising an X gate applied to one of the n qubits; 
 a first group of subsequent layers that applies BS gates to the n qubits according to a binary tree pattern, wherein each BS gate is a single parametrized 2-qubit gate; and 
 a second group of subsequent layers that that applies BS gates to the same n qubits according to an inverse of the binary tree pattern, 
 wherein a number of layers including the first layer, the first group of subsequent layers, and the second group of subsequent layers is not more than ceiling(2 log 2  (n)+1). 
 
     
     
       12. The quantum circuit of  claim 11 , wherein n is a power of 2. 
     
     
       13. The quantum circuit of  claim 11 , wherein a root node of the binary tree pattern in the first group of subsequent layers is the qubit that the X gate is applied to. 
     
     
       14. The quantum circuit of  claim 11 , wherein a root node of the binary tree pattern in the second group of subsequent layers is the qubit that the X gate is applied to. 
     
     
       15. The quantum circuit of  claim 11 , wherein a total number of qubits in the quantum circuit is not greater than n. 
     
     
       16. The quantum circuit of  claim 11 , wherein a total number of BS gates in the quantum circuit is not greater than 2n−2. 
     
     
       17. The quantum circuit of  claim 11 , wherein the BS gates in the second group of subsequent layers are conjugate gates of the BS gates in the first group of subsequent layers. 
     
     
       18. The quantum circuit of  claim 11 , wherein each BS gate in the first group of subsequent layers has a form:
     BS (θ j )=[[1,0,0,0],[0,cos(θ j ),sin(θ j ),0],[0,−sin(θ j ),cos(θ j ),0],[0,0,0,1]],
 
 
       where θ j  is an angle and j is an integer indicating a location of the BS gate in the binary tree pattern of the first group of subsequent layers. 
     
     
       19. The quantum circuit of  claim 18 , wherein each BS gate in the second group of subsequent layers has a form:
     BS   + (θ j )=[[1,0,0,0],[0,cos(θ j ),−sin(θ j ),0],[0,sin(θ j ),cos(θ j ),0],[0,0,0,1]],
 
 
       where θ j  is an angle and j is an integer indicating a location of the BS gate in the inverse binary tree pattern of the second group of subsequent layers. 
     
     
       20. The quantum circuit of  claim 11 , wherein a number of BS gates in the second group of subsequent layers is equal to a number of BS gates in the first group of subsequent layers. 
     
     
       21. A method for executing a quantum circuit, the quantum circuit for use in encoding a first n-dimensional vector representing classical data into a first quantum state, encoding a second n-dimensional vector representing classical data into a second quantum state, and determining a distance between the first n-dimensional vector and the second n-dimensional vector, the method comprising:
 executing a first layer comprising an X gate applied to one of 2n qubits; 
 executing a first group of subsequent layers that applies BS gates to the 2n qubits according to a binary tree pattern, wherein each BS gate is a single parametrized 2-qubit gate; and 
 executing an additional layer after the first group of subsequent layers that applies BS gates in parallel to pairs of qubits of the 2n qubits, wherein a first qubit in a pair is associated with the first quantum state and a second qubit in the pair is associated with the second quantum state, 
 wherein a number of layers including the first layer, the first group of subsequent layers, and the additional layer is not more than ceiling(log 2  (n)+3). 
 
     
     
       22. A non-transitory computer-readable storage medium comprising stored instructions for executing a quantum circuit, the quantum circuit for use in encoding a first n-dimensional vector representing classical data into a first quantum state, encoding a second n-dimensional vector representing classical data into a second quantum state, and determining a distance between the first n-dimensional vector and the second n-dimensional vector, the stored instructions, when executed by a computing system, cause the computing system to perform operations comprising:
 executing a first layer comprising an X gate applied to one of 2n qubits; 
 executing a first group of subsequent layers that applies BS gates to the 2n qubits according to a binary tree pattern, wherein each BS gate is a single parametrized 2-qubit gate; and 
 executing an additional layer after the first group of subsequent layers that applies BS gates in parallel to pairs of qubits of the 2n qubits, wherein a first qubit in a pair is associated with the first quantum state and a second qubit in the pair is associated with the second quantum state, 
 wherein a number of layers including the first layer, the first group of subsequent layers, and the additional layer is not more than ceiling(log 2  (n)+3). 
 
     
     
       23. A method for executing a quantum circuit, the quantum circuit for use in encoding a first n-dimensional vector representing classical data into a first quantum state, encoding a second n-dimensional vector representing classical data into a second quantum state, and determining a distance between the first n-dimensional vector and the second n-dimensional vector, the method comprising:
 executing a first layer comprising an X gate applied to one of n qubits; 
 executing a first group of subsequent layers that applies BS gates to the n qubits according to a binary tree pattern, wherein each BS gate is a single parametrized 2-qubit gate; and 
 executing a second group of subsequent layers that that applies BS gates to the same n qubits according to an inverse of the binary tree pattern, 
 wherein a number of layers including the first layer, the first group of subsequent layers, and the second group of subsequent layers is not more than ceiling(2 log 2  (n)+1). 
 
     
     
       24. A non-transitory computer-readable storage medium comprising stored instructions for executing a quantum circuit, the quantum circuit for use in encoding a first n-dimensional vector representing classical data into a first quantum state, encoding a second n-dimensional vector representing classical data into a second quantum state, and determining a distance between the first n-dimensional vector and the second n-dimensional vector, the stored instructions, when executed by a computing system, cause the computing system to perform operations comprising:
 executing a first layer comprising an X gate applied to one of n qubits; 
 executing a first group of subsequent layers that applies BS gates to the n qubits according to a binary tree pattern, wherein each BS gate is a single parametrized 2-qubit gate; and 
 executing a second group of subsequent layers that that applies BS gates to the same n qubits according to an inverse of the binary tree pattern, 
 wherein a number of layers including the first layer, the first group of subsequent layers, and the second group of subsequent layers is not more than ceiling(2 log 2  (n)+1).